Quantum states of intramolecular nuclear motion with large amplitudes: Pseudorotation of trigonal bipyramidal molecules

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Abstract
A method for the variational calculation of multidimensional eigenstates of a Hamiltonian for the nonharmonic bounded nuclear motion in a molecule is presented. For the case where the potential energy along an internal reference coordinate ξ is strongly nonharmonic, while perpendicular to this coordinate only harmonic terms with ξ−dependent force constants and displacements appear, the secular matrix elements can be calculated from general selection rules with respect to vibrational quantum numbers and one−dimensional integrals. The diagonalization was performed by an iterative procedure. The formalism was applied to the Berry pseudorotation of the trigonal bipyramidal CH3PF4 molecule where the energy surface was obtained from specially adapted semiempirical calculations. The rate of the rearrangement process was calculated as a function of temperature using a simplified model for the time dependence of the system. Nonadiabatic effects are included.